Çoklu Doğrusal Regresyon Çözümlemesinde Farklı Korelasyon Yapılarında %80 Güç İçin Örneklem Büyüklüğünün Belirlenmesi

Abstract

Parmaksız, A., Determination of Sample Size for 80% Power in Different Correlation Structures in Multiple Linear Regression Analysis, Hacettepe University Graduate School of Health Scıences Doctor of Philosophy Thesis in Biostatistics, Ankara, 2019. Nowadays, statistical inference methods are used in almost all science branches. As for linear regression analysis, it is one of the oldest and the most commonly used method among these inferential methods. If findings obtained from statistical methods, parameters estimated and inferences are to be sound and reliable, assumptions related to these methods must be ensured. In order to avoid these errors checklists concerning to the qualifications which a study should have are utilized. In today’s studies giving only the p values is not regarded as acceptable, instead the information like standart error, confidence interval, effect size and statistical power is asked to be presented in the report of the study. In this context, it is very important for the sample size to be determined correctly so that a planned linear regression analysis can have enough statistical power. In linear regression analyses, sample size is determined with simple and practical approaches called Rules of Thumb. However, sample sizes determined with rules of thumb do not convey any information about the power of the study. Therefore, for a planned linear regression analysis sample size should be calculated with effect size and power calculation methods. In this study, sample size was determined for 80% power in different correlation structures in multiple linear regression analysis, using simulation method. For the desired statistical power sample sizes obtained with both rules of thumb approach and simulation study was compared and discussed. In the thesis, it is seen that finger-counting methods could not provide decent powerful sample size except few cases, and that preferring ρ2 as the effect size for factor estimates to determine the sample size is not the correct choice. It is also understood that the required accurate sample size in multiple linear regression analysis is affected by the number of independent variables, practical purpose of the model and the correlations between the variables. Moreover, it is demonstrated that the tables confronted in the literature are not sufficient to determine the accurate sample size due to gaining various sample sizes as a result of correlation change.